Heat the olive oil in a large skillet over medium-high heat. Add the lamb shoulder pieces and brown them on all sides for about 6 minutes total. Transfer the lamb to the slow cooker.
Add the diced onion, minced garlic, and sliced carrots to the same skillet. Cook for 4 minutes until the onion starts to soften, then scrape everything into the slow cooker.
Pour the diced tomatoes with their juices and the beef broth into the slow cooker. Add the Kalamata olives, fresh thyme leaves, salt, and black pepper.
Stir the ingredients gently to combine, then cover the slow cooker. Cook on low for 8 hours until the lamb is fork-tender.
Taste the broth and adjust salt or pepper if needed before serving.